Chapter 15

If three coins are tossed, find the probability of getting two heads and one tail. \(\frac{3}{8}\)

How many three-person committees can be formed from a group of nine people? 84

In how many ways can six people be seated in a row of six seats? 720

How many two-card hands can be dealt from a deck of 52 playing cards? 1326

In how many ways can Al, Bob, Carlos, Don, Ed, and Fern be seated in a row of six seats if \(\mathrm{Al}\) and Bob want to sit side by side? 240

In how many ways can \(\mathrm{Al}\), \(\mathrm{Bob}\), Carlos, Don, Ed, and Fern be seated in a row of six seats if \(\mathrm{Al}\) and Bob want to sit side by side? 240

What is the probability of getting a sum of 8 with one roll of a pair of dice? \(\frac{5}{36}\)

Toss a pair of dice. What is the probability of not getting a double? \(\frac{5}{6}\)

Two dice are tossed. Find the proba- bility of rolling each of the following events: A sum of 6 \(\frac{5}{36}\)

How many three-letter permutations can be formed from the first eight letters of the alphabet (a) if repetitions are not allowed? (b) if repetitions are allowed? (a) 336 (b) 512

In how many ways can Amy, Bob, Cindy, Dan, and Elmer be seated in a row of five seats so that neither Amy nor Bob occupies an end seat? 36

Solve each problem.Toss a pair of dice. What is the probability of not getting a double? \(\frac{5}{6}\)

What is the probability of getting a sum greater than 5 with one roll of a pair of dice? \(\frac{13}{18}\)

The probability that a certain horse will win the Kentucky Derby is \(\frac{1}{20}\). What is the probability that it will lose the race? \(\frac{19}{20}\)

In a seven-team baseball league, in how many ways can the top three positions in the final standings be filled? 210

In how many ways can Al, Bob, Carlos, Don, Ed, and Fern be seated in a row of six seats if \(\mathrm{Al}\) and Bob are not to be seated side by side? [Hint: Either \(\mathrm{Al}\) and Bob will be seated side by side or they will not be seated side by side.] 480

Solve each problem.The probability that a certain horse will win the Kentucky Derby is \(\frac{1}{20}\). What is the probability that it will lose the race? \(\frac{19}{20}\)

Find the probability of rolling each of the following events:A sum of \(11 \quad \frac{1}{18}\)

Aimée, Brenda, Chuck, Dave, and Eli are randomly seated in a row of five seats. Find the probability that Aimée and Chuck are not seated side by side. \(\frac{3}{5}\)

One card is randomly drawn from a deck of 52 playing cards. What is the probability that it is not an ace? \(\frac{12}{13}\)

In how many ways can \(\mathrm{Al}, \mathrm{Bob}\), Carol, Dawn, and Ed be seated in a row of five chairs if \(\mathrm{Al}\) is to be seated in the middle chair?

Solve each problem.One card is randomly drawn from a deck of 52 playing cards. What is the probability that it is not an ace? \(\frac{12}{13}\)

In how many ways can Al, Bob, Carol, Dawn, and Ed be seated in a row of five chairs if \(A l\) is to be seated in the middle chair? 24

Four girls and three boys are to be randomly seated in a row of seven seats. Find the probability that the girls and boys will be seated in alternating seats. \(\frac{1}{35}\)

Six coins are tossed. Find the probability of getting at least two heads. \(\frac{57}{64}\)

In a baseball league of nine teams, how many games are needed to complete the schedule if each team plays 12 games with each other team? 432

In how many ways can three letters be dropped in five mailboxes? 125

Solve each problem.Six coins are tossed. Find the probability of getting at least two heads. \(\frac{57}{64}\)

A two-person committee is chosen at random from a group of four men and three women. Find the probability that the committee contains at least one man. \(\frac{6}{7}\)

Six coins are tossed. Find the probability of getting at least two heads. \(\frac{57}{64}\)

How many committees consisting of four women and four men can be chosen from a group of seven women and cight men? 2450

In how many ways can five letters be dropped in three mailboxes? 243

Two cards are randomly chosen from a deck of 52 playing cards. What is the probability that two jacks are drawn? \(\frac{1}{221}\)

How many three-element subsets containing one vowel and two consonants can be formed from the set \(\mid a, b, c\), d, e, f, g, h, i\\}? 45

In how many ways can four letters be dropped in six mailboxes so that no two letters go in the same box? 360

Solve each problem.A two-person committee is chosen at random from a group of four men and three women. Find the probability that the committee contains at least one man. \(\frac{6}{7}\)

Each arrangement of the six letters of the word CYCLIC is put on a slip of paper and placed in a hat. One slip is drawn at random. Find the probability that the slip contains an arrangement with the \(Y\) at the beginning. \(\frac{1}{6}\)

One card is drawn from a standard deck of 52 playing cards. Find the probability of each of the following events: \text { A heart is drawn. } \frac{1}{4}

Five associate professors are being considered for promotion to the rank of full professor, but only three will be promoted. How many different combinations of three could be promoted? 10

Solve each problem.A three-person committee is chosen at random from a group of seven women and five men. Find the probability that the committee contains at least one man. \(\frac{37}{44}\)

In how many ways can six letters be dropped in four mailboxes so that no two letters go in the same box? Impossible

A committee of three is randomly chosen from one man and six women. What is the probability that the man is not on the committee? \(\frac{4}{7}\)

\text { A king is drawn. } \frac{1}{13}

How many numbers of four different digits can be formed from the digits \(1,2,3,4,5,6,7,8\), and 9 if each number must consist of two odd and two even digits? 1440

If five coins are tossed, in how many ways can they fall? 32

Find the probability of each of the following events:A king is drawn. \(\frac{1}{13}\)

A four-person committee is selected at random from the eight people Alice, Bob, Carl, Dee, Enrique, Fred, Gina, and Hilda. Find the probability that Alice or Bob, but not both, is on the committee. \(\frac{4}{7}\)

How many three-element subsets containing the letter A can be formed from the set \(\\{A, B, C, D, E, F\\}\) ? 10

If three dice are tossed, in how many ways can they fall? 216

Find the probability of each of the following events:A spade or a diamond is drawn. \(\frac{1}{2}\)